Some general convergence theorems on fixed points
- Authors: Panicker, Rekha Manoj
- Date: 2014
- Subjects: Fixed point theory , Convergence , Coincidence theory (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5426 , http://hdl.handle.net/10962/d1013112
- Description: In this thesis, we first obtain coincidence and common fixed point theorems for a pair of generalized non-expansive type mappings in a normed space. Then we discuss two types of convergence theorems, namely, the convergence of Mann iteration procedures and the convergence and stability of fixed points. In addition, we discuss the viscosity approximations generated by (ψ ,ϕ)-weakly contractive mappings and a sequence of non-expansive mappings and then establish Browder and Halpern type convergence theorems on Banach spaces. With regard to iteration procedures, we obtain a result on the convergence of Mann iteration for generalized non-expansive type mappings in a Banach space which satisfies Opial's condition. And, in the case of stability of fixed points, we obtain a number of stability results for the sequence of (ψ,ϕ)- weakly contractive mappings and the sequence of their corresponding fixed points in metric and 2-metric spaces. We also present a generalization of Fraser and Nadler type stability theorems in 2-metric spaces involving a sequence of metrics.
- Full Text:
- Date Issued: 2014
- Authors: Panicker, Rekha Manoj
- Date: 2014
- Subjects: Fixed point theory , Convergence , Coincidence theory (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5426 , http://hdl.handle.net/10962/d1013112
- Description: In this thesis, we first obtain coincidence and common fixed point theorems for a pair of generalized non-expansive type mappings in a normed space. Then we discuss two types of convergence theorems, namely, the convergence of Mann iteration procedures and the convergence and stability of fixed points. In addition, we discuss the viscosity approximations generated by (ψ ,ϕ)-weakly contractive mappings and a sequence of non-expansive mappings and then establish Browder and Halpern type convergence theorems on Banach spaces. With regard to iteration procedures, we obtain a result on the convergence of Mann iteration for generalized non-expansive type mappings in a Banach space which satisfies Opial's condition. And, in the case of stability of fixed points, we obtain a number of stability results for the sequence of (ψ,ϕ)- weakly contractive mappings and the sequence of their corresponding fixed points in metric and 2-metric spaces. We also present a generalization of Fraser and Nadler type stability theorems in 2-metric spaces involving a sequence of metrics.
- Full Text:
- Date Issued: 2014
Lattice-valued uniform convergence spaces the case of enriched lattices
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
- Full Text:
- Date Issued: 2008
- Authors: Craig, Andrew Philip Knott
- Date: 2008
- Subjects: Lattice theory , Uniform spaces , Convergence
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5411 , http://hdl.handle.net/10962/d1005225 , Lattice theory , Uniform spaces , Convergence
- Description: Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.
- Full Text:
- Date Issued: 2008
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